I don't know why your life depends on answering a phone call, but I could think of two ways to do it.

Method 1: Hack into the phone. Open the phone casing and check out its circuit. It would surely have a buzzer/speaker which makes sound during an incoming call. So you will get a voltage across this speaker whenever there is a phone call. Now to answer the phone we will have a switch which has to be released (made open). So we have to build a circuit that detects this voltage across the speaker open the switch automatically. I am not a big fan of this method though

Method 2: This is my fav and would work like a charm, but you have to either get a SIM card for that number of divert all calls to a SIM card. Then this SIM card can be installed in a GSM module and interfaced woth a MCU like Arduino. With few lines of code, you can make the Arduino automatically attend all the calls to this number or even specify from which which number it should attend. I have already tired this out with one additional feature and that is you can interface a voice module with it and a pre-recorded voice message will be played as soon as the call is attended by the Arduino!